Efficient and Distributed Large-Scale Point Cloud Bundle Adjustment via Majorization-Minimization

Abstract: Point cloud bundle adjustment is critical in large-scale point cloud mapping. However, it is both computationally and memory intensive, with its complexity growing cubically as the number of scan poses increases. This paper presents BALM3.0, an efficient and distributed large-scale point cloud bundle adjustment method. The proposed method employs the majorization-minimization algorithm to decouple the scan poses in the bundle adjustment process, thus performing the point cloud bundle adjustment on large-scale data with improved computational efficiency. The key difficulty of applying majorization-minimization on bundle adjustment is to identify the proper surrogate cost function. In this paper, the proposed surrogate cost function is based on the point-to-plane distance. The primary advantages of decoupling the scan poses via a majorization-minimization algorithm stem from two key aspects. First, the decoupling of scan poses reduces the optimization time complexity from cubic to linear, significantly enhancing the computational efficiency of the bundle adjustment process in large-scale environments. Second, it lays the theoretical foundation for distributed bundle adjustment. By distributing both data and computation across multiple devices, this approach helps overcome the limitations posed by large memory and computational requirements, which may be difficult for a single device to handle. The proposed method is extensively evaluated in both simulated and real-world environments. The results demonstrate that the proposed method achieves the same optimal residual with comparable accuracy while offering up to 704 times faster optimization speed and reducing memory usage to 1/8. Furthermore, this paper also presented and implemented a distributed bundle adjustment framework and successfully optimized large-scale data (21,436 poses with 70 GB point clouds) with four consumer-level laptops.

Efficient and Distributed Large-Scale Point Cloud Bundle Adjustment via Majorization-Minimization

The paper titled "Efficient and Distributed Large-Scale Point Cloud Bundle Adjustment via Majorization-Minimization" by Rundong Li et al. presents BALM3.0, a computationally efficient and scalable approach for point cloud bundle adjustment leveraging the majorization-minimization (MM) algorithm. The paper addresses a critical challenge in the field of robotics and 3D mapping: the substantial computational and memory resources required for point cloud bundle adjustment, especially as the number of scan poses increases.

Problem and Approach

Point cloud bundle adjustment is an optimization problem that aims to jointly estimate LiDAR scan poses and map parameters to achieve consistent and accurate 3D maps. Traditional methods suffer from high computational complexity, intensifying cubically with the number of scan poses due to the dense Hessian matrix involved in the optimization process. The BALM2 method, for instance, although efficient, still faces prohibitive computational demands for extensive scenes.

To overcome these limitations, the authors propose BALM3.0, which employs the MM algorithm to decouple scan poses within the bundle adjustment process. This decoupling reduces the complexity of the optimization task from cubic to linear, thereby significantly enhancing computational efficiency. The MM approach simplifies the optimization by introducing a surrogate cost function, which is easier to minimize and serves as an upper bound to the original cost function. Improvements on the surrogate function guarantee improvements on the original problem.

The surrogate cost function formulation makes use of the point-to-plane distance metric, enabling complete decoupling of state variables related to scan poses. This simplification results in a block-diagonal Hessian matrix, facilitating rapid and parallel processing across multiple devices, thus permitting distributed optimization.

Numerical Results

The method was extensively evaluated in simulated and real-world environments, achieving significant improvements in optimization speed and memory efficiency without compromising accuracy. Experimental results demonstrated that BALM3.0 attains the same optimal residual with comparable accuracy as state-of-the-art methods while reducing optimization speed by up to 704 times and memory usage to one-eighth. For instance, it was successfully implemented to optimize 21,436 poses with 70 GB of point clouds using four consumer-level laptops.

Implications and Future Work

The implications of this research are profound for practical applications requiring large-scale environment mapping, such as autonomous driving, city modeling, and geospatial information systems. By distributing data and computations across multiple devices, BALM3.0 alleviates the constraints imposed by the memory and computational capacities of individual machines, making large-scale point cloud mapping more accessible and practical.

Theoretically, this paper introduces a novel approach to point cloud bundle adjustment that could inspire further developments in distributed optimization techniques within the domain. Future research could build upon this work by exploring more refined surrogate functions or integrating this method with other mapping frameworks to enhance robustness and adaptability to various environmental conditions and sensor types.

In summary, the authors present a well-documented and effective solution to a persistent challenge in 3D mapping, contributing significantly to both practical methodologies and theoretical understandings of distributed optimization in bundle adjustment tasks.